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3 years ago

A line passes through the two points: (1, 10) and (6,5).

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

5 0

Answer:

(a). - 1 ; (b). y = - x + 11

Step-by-step explanation:

(1, 10)

(6, 5)

(a). m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$ = $\frac{5-10}{6-1}$ = - 1

(b). y - 5 = - 1(x - 6)

y = - x + 11

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Consider a discrete random variable x with pmf px (1) = c 3 ; px (2) = c 6 ; px (5) = c 3 and 0 otherwise, where c is a positive

PtichkaEL [24]

Looks like the PMF is supposed to be

$\mathbb P(X=x)=\begin{cases}\dfrac c3&\text{for }x\in\{1,5\}\\\\\dfrac c6&\text{for }x=2\\\\0&\text{otherwise}\end{cases}$

which is kinda weird, but it's not entirely clear what you meant...

Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:

$\displaystyle\sum_{x\in\{1,2,5\}}\mathbb P(X=x)=\dfrac c3+\dfrac c6+\dfrac c3=\dfrac{5c}6=1\implies c=\dfrac65$

Next,

$\mathbb P(X>2)=\mathbb P(X=5)=\dfrac c3=\dfrac25$

$\mathbb E(X)=\displaystyle\sum_{x\in\{1,2,5\}}x\,\mathbb P(X=x)=\dfrac c3+\dfrac{2c}6+\dfrac{5c}3=\dfrac{7c}3=\dfrac{14}5$

$\mathbb V(X)=\mathbb E\bigg((X-\mathbb E(X))^2\bigg)=\mathbb E(X^2)-\mathbb E(X)^2$
$\mathbb E(X^2)=\displaystyle\sum_{x\in\{1,2,5\}}x^2\,\mathbb P(X=x)=\dfrac c3+\dfrac{4c}6+\dfrac{25c}3=\dfrac{28c}3=\dfrac{56}5$
$\implies\mathbb V(X)=\dfrac{56}5-\left(\dfrac{14}5\right)^2=\dfrac{84}{25}$

If $Y=X^2+1$ , then $X^2=Y-1\implies X=\sqrt{Y-1}$ , where we take the positive root because we know $X$ can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that $Y$ can take on the values $1^2+1=2$ , $2^2+1=5$ , and $5^2+1=26$ . At these values of $Y$ , we would have the same probability as we did for the respective value of $X$ . That is,

$\mathbb P(Y=y)=\begin{cases}\dfrac c3&\text{for }y=2\\\\\dfrac c6&\text{for }y=5\\\\\dfrac c3&\text{for }y=26\\\\0&\text{otherwise}\end{cases}$

Part (5) is incomplete, so I'll stop here.

8 0

3 years ago

Find the solution set. |x| = -4 A. { } B. {-2, 2} C. {-4, 4} D. {-16, 16}

Ray Of Light [21]

Answer:

A. { }

Step-by-step explanation:

Absolute value cannot be less than zero.

-4 < 0

There is no solution for x, ∈, R.

Hope this helps.

6 0

3 years ago

Whats is 0.000001 written as a power of ten

siniylev [52]

You need to move the decimal point to be at 1.

Since this is a decimal, the power will be negative.

I had to move the decimal 6 places.

So,

1^-6

I hope this helps!
~kaikers

8 0

2 years ago

Which sequence of transformations produces R'S'T' from RST? On a coordinate plane, triangle R S T has points (0, 0), (negative 2

arsen [322]

Answer:

Step-by-step explanation:

Given is a triangle RST and another triangle R'S'T' tranformed from RST

Vertices of RST are (0, 0), (negative 2, 3), (negative 3, 1).

Vertices of R'S'T' are (2, 0), (0, negative 3), (negative 1, negative 1).

Comparing the corresponding vertices we find that x coordinate increased by 2 while y coordinate got the different sign.

This indicates that there is both reflection and transformation horizontally to the right by 2 units

So first shifted right by 2 units so that vertices became

(2,0) (0,3) (-1,1)

Now reflected on the line y=0 i.e. x axis

New vertices are

(2,0) (0,-3) (-1,-1)

8 0

3 years ago

Tanya says .53 is greater than .7 because 53 is greater than 7 Can you explain her mistake?

sergey [27]

Take 0.53 and 0.7 by 100 to make them percents. 0.53 times 100 is 53% and 0.7 time 100 is 70%. so 0.7>0.53

4 0

3 years ago

Read 2 more answers